The relaxation parameters for the higher order moments \(\omega _j\) , where \(j=6,7\)  and 8 influence numerical stability (see e.g., [1]}) and are set to unity in this work. It may be noted that the correction terms given in Eqs. (REF ) and (REF ) for the diagonal components of the second order moment equilibria are dependent on the grid aspect ratio \(a\)  and the speed of sound \(c_s\) , both of which are free parameters of our formulation, with the latter adjusted based on the choice of the former to maintain numerical stability. Equation (REF ) implies that no additional corrections are necessary for the off-diagonal second order moment equilibria for the rectangular LB formulation. Moreover, the transport coefficients given in Eqs. (REF ) and () are not parameterized by the grid aspect ratio, and maintain the simple expressions applicable for the square lattice. It may be noted that, as a special case, when we set \(a=1\)  and the speed of sound \(c_s=1/\sqrt{3}\) , the previous results for the square lattice are recovered (see e.g., [2]}) and the isotropy corrections (Eqs. (REF ) and (REF )) vanish.
